Bonita with ASP.net Core
I guess that "ASP.net Core Web API" are REST API that you can call using HTTP requests.
If you confirm that you should be able to call such API from your forms and pages created with the UI Designer using a "External API" variable (that will perform a GET request on the API) or use a "Button widget" to perform GET, PUT, POST and DELETE requests.
Also an alternative would be to create a REST API extension that can act as a proxy calling your APIs.
If you have any publicly available APIs I can try to provide an example.
I'm using External API variable, I traced the requests on fiddler, I can see the request of my api with its response, but results are not shown on dropdownlist.
I changed the api to another ASP.Net api (not core) result bind successfully